@mmcdara Thanks to both of you. I think the ColumnGraph is the appropriate command here, because I am not going to produce a Histogram by having something counted. I have the height of the columns already. Your file was however valuable afterall, mmcdara! I have tried writing the appropriate command for my easy purpose (see attached file).  I am however surprised that it cannot be done in a more easy default way - if that is the case. I have to fiddle with an offset option. I was expecting Maple to be able to easily produce a default plot with columns just by having the letters on the x-axis and the frequencies - and producing equally spaced columns with the letters in the middle. Or maybe I have overlooked something?

The help page for ColumnGraph wasn't to much help. In contrast to what is usually seen in the help pages, it started out with some very difficult scene, and it was hard for me to deduce anything at all for my easy situation - which again then doesn't seem to be that easy afterall. 

Erik

ColumnGraphs.mw

@tomleslie Yes it works that way, but still is using the properties of the normal distribution, i. e. the mean can be put "outside" which makes it possible to accomplish the job by just creating one single sample. Maybe I have confused the situation by connecting my more general question to this specific problem, which can be solved more easily. I think I will close my question here and get back if I later stumble upon a situation where this shortcut is not possible. 

Erik

Thanks to both of you, Carl Love and Acer. Very valuable information indeed.

Erik

@Daniel Skoog Thanks for the information, Daniel. 

@Kitonum Thanks a lot, Kitonum. I appreciate it!

Regards,

Erik

@Carl Love Indeed very compact. Just what I was looking for. Thanks a lot!

Erik

@acer For the sake of completeness in this specific situation it would however be appropriate to have all possible values of X listed. Obviously the difference only show up for small sample sizes, where a frequency might turn out to be 0. 

@acer Thanks to both of you. It is also apparent that when choosing big samples, your code is qite a lot faster!

Erik

@acer In addition to your fine histograms, I wanted to calculate the actual sample frequencies. With your list M of possible values for the Random Variable X I did it this way:

Isn't there an even more simple way of doing it? I mean I was surprised not to be able to find a command in the Statistics package which could give the frequencies of a list of numbers right away. Maybe I overlooked something?

Erik

@mmcdara Very illustrative indeed!!

@acer Big thanks to you and mmcdara for a splendid work! It has certainly helped my investigations in the department of Random Variables. I guess it isn't possible to easily calculate the probability distributions of Random Variables built on other Random Variables in general. The possibilities are simply too complex. In the case of finite Sample Space you have however shown a way to search or go through all possible outcomes and that way get to the probability distribution. I think I am empty for more questions at the moment :)

@acer Your way of making an animation was indeed ingenious. So now my questions regarding samples are settled. 

I am still working on building intuition in relation to how Maple handles Random Variables. Beside being able to calculate Mean and Variance, I am interested in calculating probablities (including cumulative ones - CDF). In the present example with the player against the banker I cannot make it work. I receive a FAIL. I guess it happens because it is necessary to "invert the problem" internally and that Maple isn't capable of doing so - directly at least. In the following let X equal the profit in one play, viewed from the Players viewpoint. Manually one need to ask: What are the possible combinations of dice, which will yield the value 3 for X? The answer is (2,5), (3,6), (5,2) and (6,3). Each with probability 1/36, so the correct answer is 4/36. But Maple can't do it directly. Is there a smart non-ad hoc way to make problems like this work? (one which doesn't require the user to know the answer beforehand). I tried the technique with the old Random Variable Y = Dice1+Dice2, and it works! But here Maple doesn't need to do "back-tracking" in order to compute the probabilities ...

Best regards,

Erik

@acer That was impressing! I will have to look into that one tomorrow. Thanks a lot!

Erik

@mmcdara This is indeed nice. Thank you!

@tomleslie Yes one need to be careful about algebraic expressions involving those calls for random draws :)

Now that histograms for samples of the Random Variable connected to the Player/banker (call it X) is established, I was looking for a way to define or create the Random Variable X in Maple in the hope Maple could itself calculate the theoretical Mean and Variance (not for a sample). I looked at the commands Distribution and RandomVariable in the Statistics package. The few examples in the Help menu didn't help me much, though. Maybe it is not something one should do here?

Erik